Texture baking is not in sync
You can achieve this using a second UV map (Cycles).


Use the "+" button in the UV map list: this will create a copy of your original (selected) UV map.
Arrange the UVs as you need in this second UV map.
Keep the first UV map as rendering target (the camera button on the right is still active for it)
Select the second UV map (this selection will indicate this second UV map will be used as bake target, the same way the target image node needs to be selected)
Bake